Test for divisibility of numbers by 3, 6, 4 and 8
(d) Divisibility by 3
If the sum of the digits of a number is divisible by 3, then the number will be divisible by 3. In other words, if the sum of the digits of a number is multiple of 3, then the number will be divisible by 3.
Examples of numbers divisible by 3
(i) 12: Test of divisibility of 12 by 3.
The sum of digits of 12 = 1 + 2 = 3
Since, the sum of digits of 12 which is equal to 3 is divisible by 3, hence 12 is divisible by 3.
12 ÷ 3 = 4
(ii) 13: Test of divisibility of 13 by 3.
The sum of digits of 13 = 1 + 3 = 4
Since, the sum of digits of 13 which is equal to 4 is not divisible by 3, hence 13 is not divisible by 3.
(iii) 15: Test of divisibility of 15 by 3.
The sum of digits of 15 = 1 + 5 = 6
Since, the sum of digits of 15 which is equal to 6 is divisible by 3, hence 15 is divisible by 3.
15 ÷ 3 = 5
(iii) 16: Test of divisibility of 16 by 3.
The sum of digits of 16 = 1 + 6 = 7
Since, the sum of digits of 16 = 1 + 6 = 7, is not a multiple of 3, hence 16 is not divisible by 3.
(iv) 57: Test of divisibility of 57 by 3.
The sum of digits of 57 = 5 + 7 = 12
Since, the sum of digits of 57 which is equal to 12 is divisible by 3, hence 57 is divisible by 3.
57 ÷ 3 = 19
(e) Divisibility by 6
If a number is divisible by 2 and 3 both, then the number will be divisible by 6.
Example: Test of divisibility of numbers by 6
(i) 8: Eight (8) has even number at its ones place, hence it is divisible by 2. But 8 is not divisible by 3, hence 8 (eight) is not divisible by 6.
(ii) 12:
Test of divisibility of 12 by 2
We know that numbers having even number at their ones place are divisible by 2.
Since, 12 has an even number at its ones place, hence 12 is divisible by 2
Test of divisibility of 12 by 3
We know that, if the sum of the digits of a number is multiple of 3, then the number is divisible by 3.
Here, 12 = 1 + 2 = 3
Since, the sum of the digits of 12 which is equal to 3 is a multiple of 3, thus, 12 is divisible by 3
Test of divisibility of 12 by 6
Since, 12 is divisible by 2 and 3 both, thus 12 is divisible by 6.
12 ÷ 6 = 2
(iii) 24:
Test of divisibility of 24 by 2
We know that numbers having even number at their ones place are divisible by 2.
Since, 24 has an even number at its ones place, hence 24 is divisible by 2
Test of divisibility of 24 by 3
We know that, if the sum of the digits of a number is multiple of 3, then the number is divisible by 3.
Here, 24 = 2 + 4 = 6
Since, the sum of the digits of 24 which is equal to 6 is a multiple of 3, thus, 24 is divisible by 3
Test of divisibility of 24 by 6
Since, 24 is divisible by 2 and 3 both, thus 24 is divisible by 6.
24 ÷ 6 = 4
(f) Divisibility by 4 of numbers having three digits or more
It is very easy to find the divisibility of numbers having one or two digits by 4. But it appears a bit difficult to check the divisibility of numbers having more than two digits.
If the last two digits of a number having more than two digits, is divisible by 4, then the number will be divisible by 4.
Example: Test of divisibility by 4
(i) 324
24 is the last two digits of the number 324 is divisible by 4, hence the number 324 is divisible by 4.
324 ÷ 4 = 81
(ii) 328
28 is the last two digits of the number 328 is not divisible by 4, hence the number 328 is not divisible by 4.
(iii) 3332
32 is the last two digits of the number 3332 is divisible by 4, hence the number 3332 is divisible by 4.
3332 ÷ 4 = 833
(f) Divisibility by 8 of numbers having four digits or more
The divisibility by 8 for numbers having four or more digits can be checked easily.
If the sum of the last three digits of a number having four or more digits is divisible by 8, then the number will be divisible by 8.
Examples to test divisibility of numbers having four or more digits by 8
(i) 3616:
In the number 3616, the last three digits 616 is divisible by 8, and hence the number 3616 is divisible by 8.
616 ÷ 8 = 77
And, hence 3616 ÷ 8 = 452
(ii) 3800:
In the number 3800, the last three digits 800 is divisible by 8, and hence the number 3800 is divisible by 8.
800 ÷ 8 = 100
And, hence 3800 ÷ 8 = 475
(iii) 1896:
In the number 1896, the last three digits 896 is divisible by 8, and hence the number 1896 is divisible by 8.
896 ÷ 8 = 112
And, hence 1896 ÷ 8 = 237